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Beliebt Rechnen >

integral from 0 to x of ylog_{10}(y)

Lösung

\int_{0}^{x} y lo g_{10} (y) d y

Lösung

\frac{x ^{2} lo g _{10} ( x )}{2} - \frac{x ^{2}}{4 ln ( 10 )}

Schritte zur Lösung

\int_{0}^{x} y lo g_{10} (y) d y

Wende die partielle Integration an

= [\frac{1}{2} y^{2} lo g_{10} (y) - \int \frac{y}{2 ln ( 10 )} d y]_{0}^{x}

\int \frac{y}{2 ln ( 10 )} d y = \frac{y ^{2}}{4 ln ( 10 )}

= [\frac{1}{2} y^{2} lo g_{10} (y) - \frac{y ^{2}}{4 ln ( 10 )}]_{0}^{x}

Berechne die Grenzen:

\frac{1}{2} x^{2} lo g_{10} (x) - \frac{x ^{2}}{4 ln ( 10 )}

= \frac{1}{2} x^{2} lo g_{10} (x) - \frac{x ^{2}}{4 ln ( 10 )}

Vereinfache

= \frac{x ^{2} lo g _{10} ( x )}{2} - \frac{x ^{2}}{4 ln ( 10 )}

Beliebte Beispiele

sum from n=3 to infinity of (4^n)/(7^n)

n = 3 \sum \infty \frac{4 ^{n}}{7 ^{n}}

integral of x^4y^3

\int x^{4} y^{3} d y

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integral from-1 to 1 of (-x^2+1)^2

\int_{- 1}^{1} (- x^{2} + 1)^{2} d x